An exponential function does not create a linear shape on a graph. Instead, it produces a curve that either rises or falls rapidly, depending on whether the base of the exponent is greater than or less than one. The graph is characterized by its continuous and smooth nature, exhibiting either exponential growth or decay. Additionally, it does not form any circular or parabolic shapes, which are seen in other types of functions.
If the Object is falling at a constant velocity the shape of the graph would be linear. If the object is falling at a changing velocity (Accelerating) the shape of the graph would be exponential- "J' Shape.
An exponential graph typically exhibits a J-shaped curve. For exponential growth, the graph rises steeply as the value of the variable increases, while for exponential decay, it falls sharply and approaches zero but never quite reaches it. The key characteristic is that the rate of change accelerates or decelerates rapidly, depending on whether it is growth or decay.
shape
An exponential graph typically has a characteristic J-shaped curve. It rises steeply as the value of the independent variable increases, particularly for positive bases greater than one. If the base is between zero and one, the graph decreases towards the x-axis but never touches it, creating a decay curve. Overall, exponential graphs show rapid growth or decay depending on the base value.
The graph of a linear function is a straight line. It can have a positive slope, indicating an upward trend, or a negative slope, indicating a downward trend. The line can also be horizontal if the function has a slope of zero, representing a constant value. The overall shape is determined by the function's slope and y-intercept.
If the Object is falling at a constant velocity the shape of the graph would be linear. If the object is falling at a changing velocity (Accelerating) the shape of the graph would be exponential- "J' Shape.
A monotonic transformation does not change the overall shape of a function's graph, but it can stretch or compress the graph horizontally or vertically.
An exponential graph typically exhibits a J-shaped curve. For exponential growth, the graph rises steeply as the value of the variable increases, while for exponential decay, it falls sharply and approaches zero but never quite reaches it. The key characteristic is that the rate of change accelerates or decelerates rapidly, depending on whether it is growth or decay.
shape
shape
An exponential graph typically has a characteristic J-shaped curve. It rises steeply as the value of the independent variable increases, particularly for positive bases greater than one. If the base is between zero and one, the graph decreases towards the x-axis but never touches it, creating a decay curve. Overall, exponential graphs show rapid growth or decay depending on the base value.
The graph of a linear function is a straight line. It can have a positive slope, indicating an upward trend, or a negative slope, indicating a downward trend. The line can also be horizontal if the function has a slope of zero, representing a constant value. The overall shape is determined by the function's slope and y-intercept.
I don't understand your question but y=3x is the function of a graph, to graph the function you would plug points into the function such as x=0, x=1, x=-1 and you would find the y values at each point so that you can graph it. In this case the graph is a parabola which has a u shape.
When you replace ( x ) with ( ax ) in the function ( f(x) ), the graph of the function undergoes a horizontal scaling. If ( a > 1 ), the graph compresses towards the y-axis; if ( 0 < a < 1 ), the graph stretches away from the y-axis. The overall shape of the graph remains the same, but the x-coordinates of all points on the graph change according to the factor ( a ).
A Guassian function has a top in the middle and it's ends reach until infinity but the graph never touches the x axis. The location of the top depends on the parameters used.
Changing the constant in a function will shift the graph vertically but will not change the shape of the graph. For example, in a linear function, changing the constant term will only move the line up or down. In a quadratic function, changing the constant term will shift the parabola up or down.
To shift a graph upward, you add a constant value to the function's output. For example, if you have a function ( f(x) ) and you want to shift its graph up by 3 units, you would change the function to ( f(x) + 3 ). This operation increases the y-coordinates of all points on the graph, effectively moving the entire graph up without changing its shape.